The eigenfunction expansion methods is used to obtain numerical Green's functions to solve for deflection of irregular-shaped classical plates. The associated eigenvalus problem allows to express the Green's function as a series of eigenfunctions which are approximated by a series of polynomials that satisfy the homogeneous boundary conditions to which the plates are subjected. A computer algebra system (Mathematica) has been extensively used to construct the approximate Green's functions consisting of polynomials, reducing substantially the amount of work involved in the calculation and achievement of the solution.